bf.dist.poisson: Poisson Distribution

In BayesForge: Bayesian Inference using 'numpyro' and 'XLA'

Poisson Distribution

Description

The **Poisson distribution** models the probability of observing a given number of events $k$ occurring in a fixed interval of time or space when these events happen independently and at a constant average rate

\lambda > 0

. It is widely used for modeling **count data**, such as the number of emails received per hour or mutations in a DNA strand per unit length. Formally,

K \sim \text{Poisson}(\lambda)

where

\lambda

is both the **mean** and **variance** of the distribution.

Usage

bf.dist.poisson(
  rate,
  is_sparse = FALSE,
  validate_args = py_none(),
  name = "x",
  obs = py_none(),
  mask = py_none(),
  sample = FALSE,
  seed = py_none(),
  shape = c(),
  event = 0,
  create_obj = FALSE,
  to_jax = TRUE
)

Arguments

rate	A numeric vector representing the average number of events.
is_sparse	(bool, optional): Indicates whether the 'rate' parameter is sparse. If 'True', a specialized sparse sampling implementation is used, which can be more efficient for models with many zero-rate components (e.g., zero-inflated models). Defaults to 'False'.
validate_args	Logical: Whether to validate parameter values. Defaults to 'reticulate::py_none()'.
name	A character string representing the name of the random variable within a model. This is used to uniquely identify the variable. Defaults to 'x'.
obs	A numeric vector or array of observed values. If provided, the random variable is conditioned on these values. If 'NULL', the variable is treated as a latent (unobserved) variable. Defaults to 'NULL'.
mask	A logical vector to mask observations.
sample	A logical value that controls the function's behavior. If 'TRUE', the function will directly draw samples from the distribution. If 'FALSE', it will create a random variable within a model. Defaults to 'FALSE'.
seed	An integer used to set the random seed for reproducibility when 'sample = TRUE'. This argument has no effect when 'sample = FALSE', as randomness is handled by the model's inference engine. Defaults to 0.
shape	A numeric vector used for shaping. When ‘sample=False' (model building), this is used with '.expand(shape)' to set the distribution’s batch shape. When 'sample=True' (direct sampling), this is used as 'sample_shape' to draw a raw JAX array of the given shape.
event	An integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
create_obj	A logical value. If 'TRUE', returns the raw BI distribution object instead of creating a sample site.
to_jax	Boolean. Indicates whether to return a JAX array or not.

Value

- When sample=FALSE, a BI Poisson distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the Poisson distribution (for direct sampling).

- When create_obj=TRUE, the raw BI distribution object (for advanced use cases).

Examples

library(BayesForge)
m=importBF(platform='cpu')
bf.dist.poisson(rate = c(0.2, 0.5, 0.8), sample = TRUE)

BayesForge documentation built on June 9, 2026, 1:09 a.m.